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Job Record #18274
TitleContinuum modelling of particulate flows in nature and industry
CategoryPhD Studentship
EmployerCardiff University - Applied Mathematics
LocationUnited Kingdom, South Glamorgan, Wales, Cardiff
InternationalYes, international applications are welcome
Closure DateFriday, February 24, 2023
Fully Funded EPSRC DTP PhD Studentship in Applied and Computational Mathematics 

Project Summary

So much of the natural and man-made world is composed of collections of discrete 
solid grains. However, there is currently no completely satisfactory theory to 
describe their motion, en masse, in the many complex flow scenarios which are 
important across industry and geophysics. Despite the challenges, a promising 
paradigm has been building over the last 20 years. Based around key 
experimental, mathematical and physical insights, continuum models for both the 
flow of dry grains and for particles suspended in a background fluid are 
beginning to mature.

In this project, the driving goal will be to develop a unified rheology spanning 
the many flow regimes that particulate materials can exhibit. Once this model 
begins to take shape, novel numerical methods will be developed to solve the 
resultant dynamical equations. This in-house code will then be applied to 
various test cases inspired by flows in nature, such as debris avalanches and 
subsea landslides, and in industry, such as hopper flows and drum mixers.

The work will be framed and motivated by key open questions such as "Is it 
useful in modelling to categorise particle flow dynamics into gas-like, liquid-
like and solid-like behaviour?", "What is the most appropriate numerical method 
to solve multi-regime particulate flow equations?" and "How does the presence of 
liquid water modify the severity of natural hazards and the efficiency of 
industrial processes?".

Research Environment

Students undertaking this project will work in a dynamic field of research with 
many opportunities for innovation and impact. Success in the project will see 
the student gain ability and confidence in many areas of applied mathematics. In 
particular, the student will work at the forefront of continuum mechanics, 
computational fluid dynamics, granular rheology, discrete element modelling, 
geophysics and engineering.

Cardiff’s School of Mathematics is home to a world-leading Applied Mathematics 
group which has fostered an outstanding postgraduate research environment. The 
latest Postgraduate Research Experience Survey (PRES) ranks it 3rd in overall 
satisfaction and 1st (out of 22 in the UK) in professional development. With 
around 15 full-time staff and PhD students and weekly seminars by international 
experts, there will be many opportunities for knowledge exchange and guidance 
throughout the project.

The successful candidate will also become member of a vibrant postgraduate 
research community, which hosts the SIAM-IMA Student Chapter at Cardiff 
University, formed by the Society for Industrial and Applied Mathematics and 
supported by the Institute of Mathematics and its Applications. They will be 
provided with a desk and a computer, and access to state-of-the-art facilities 
in the School’s purpose-built new home, Abacws, where the School moved in 
September 2021.

Training and Development Opportunities

With the funding enabled by this studentship, students will have access to many 
conferences and workshops outside Cardiff. Of particular relevance in the coming 
years are the Particles 2023 conference in Milan, the 2024 Gordon Research 
Conference in Boston and Powders & Grains 2025 in India. These activities will 
encourage the general intellectual and personal development of the student, 
leading to many transferrable skills.

To expand their mathematical knowledge beyond that offered by their specific 
project, in addition to research work, in the first two years the student will 
attend a total of 100 hours of postgraduate lecture courses run by MAGIC 
(Mathematics Access Grid Instruction and Collaboration), which is jointly 
organised remotely by 20 UK Universities. Assignments to the MAGIC courses will 
be assessed by the course lecturers.


Applicants should apply through the Cardiff University online application portal 
ematics), for a Doctor of Philosophy in Mathematics with an entry point of 
October 2023.

In the research proposal section of your application, please specify the project 
title and supervisors of this project. There is no requirement to submit a 
detailed research proposal.

In the funding section, please select "I will be applying for advertised funding 


A 1st or upper 2nd class UK Honours degree (or equivalent) or a Master’s degree 
is required in mathematics or a related subject.


Applicants for whom English is not their first language must demonstrate 
proficiency by obtaining an IELTS score of at least 6.5 overall, with a minimum 
of 5.5 in each skills component. Further acceptable qualifications can be found 


·        Curriculum vitae

·        A personal statement

·        Two completed references

·        Degree certificates and transcripts

·        Proof of English language (if applicable)


EPSRC DTP studentships are available to home and international students. Up to 
30% of our cohort can comprise international students, once the limit has been 
reached we are unable to make offers to international students.

International students will not be charged the fee difference between the UK and 
international rate. Applicants should satisfy the UKRI eligibility requirements. 

Cardiff University is committed to support students from a range of backgrounds 
and circumstances. Where needed, we will work with you to take into 
consideration reasonable project adaptations (for example to support caring 
responsibilities, disabilities, other significant personal circumstances) as 
well as flexible working and part‐time study requests, to enable greater access 
to a PhD. All our supervisors support us with this aim, so please feel 
comfortable in discussing further with the listed PhD project supervisor to see 
what is feasible.

Cardiff University is committed to supporting and promoting equality and 
diversity and to creating an inclusive environment for all. We welcome 
applications from all members of the global community irrespective of age, 
disability, sex, gender identity, gender reassignment, marital or civil 
partnership status, pregnancy or maternity, race, religion or belief and sexual 

We welcome applications for both full and part-time study and from candidates 
with non-traditional academic backgrounds. For further information about modes 
of study, please contact us.


Applicants are reminded to submit all relevant documents (transcripts, 
supporting statement, etc) by the deadline. Due to the volume of applications 
received, incomplete applications will not be considered. Shortlisted applicants 
will be invited to interview early in March 2023.
Contact Information:
Please mention the CFD Jobs Database, record #18274 when responding to this ad.
NameDr Thomas Barker
Email ApplicationYes
Record Data:
Last Modified09:59:10, Wednesday, January 25, 2023

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